The Application of Euler-Rodrigues Formula over Hyper-Dual Matrices

Creative Commons License

RAMİS Ç., YAYLI Y., Zengin I.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, cilt.15, sa.2, ss.266-276, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.36890/iejg.1127216
  • Dergi Adı: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.266-276
  • Anahtar Kelimeler: Dual numbers, hyper-dual numbers, Euler-Rodrigues formula, Euler?s theorem, THEOREM, NUMBERS
  • Ankara Üniversitesi Adresli: Evet

Özet

The Lie group over the hyper-dual matrices and its corresponding Lie algebra are first introduced in this study. One of Euler's strategies called the Euler-Rodrigues formula is applied to the matrices of hyper-dual rotations. The fundamental relationship between the hyper-dual numbers and the dual numbers allows us to apply the formula on dual lines and two intersecting real lines in the three dimensional dual and Euclidean spaces, respectively.